Connecticut, especially the town of Windsor, since the early 1820s has traditionally produced leaves for the "wrapper" and "binder" parts of cigars. The wrapper is the outermost layer of a cigar; a good wrapper is important as it makes a cigar more appealing in appearance and also effects how it burns, so high quality wrapper leaf production for premium cigars has been a prosperous industry in Windsor, Connecticut since then.

In the late 1800s Connecticut began to suffer competition from imported Sumatran tobacco. In the tropics tobacco, like coffee and tea, was often grown in the shade of trees. Plants, when grown in the shade, produce leafs that are lighter in color, thinner and more elastic (the reasons behind this are scientific rather than historical, but I can elaborate if you wish). Such leaves are particularly suited for use as wrappers and binders. Naturally the inhabits of Windsor didn't want to be out competed so in 1900 or so they began to experiment with producing tropical tobacco varieties under shade canopies made of cloth. These canopies provide myriad benefits, such as shelter from pests and frost (cloth covers are often used for these purposes in the production of other crops). Their primary purpose in this case was to imitate the growing conditions of tropical tobacco by diffusing and blocking sunlight and increasing humidity. Connecticut thus continued to export quality wrapper leaf. I'm getting this info largely from A new history of old Windsor, Connecticut

As to why this practice never caught on elsewhere in the U.S. according to this account of an early USDA experiment with growing shade tobacco in Connecticut:

With the exception of a small area of Florida and southern Georgia, where this type of tobacco was originally introduced and is still successfully grown, and of a narrow area of Donegal gravelly loam along the Susquehanna River in Pennsylvania, there are no other areas, so for as at present known, where this type of tobacco may be successfully grown..."

Indeed, Windsor is still known for its high quality soil.